In terms of the best polynomial approximations in the multiple Haar basis, we obtain a constructive characteristic of the Hölder classes Hpα of functions defined on the unit cube \( \mathbb{I} \)d of the space ℝd under the restriction \( 0 . We also solve the problem of order estimates of the best m-term approximations in the Haar basis of classes Hpα in the Lebesgue spaces Lq(\( \mathbb{I} \)d).